Dissipativity Theory for Switched Systems

A frame work of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up. The exchange of "energy" between the activated subsystem and an inactivated subsystem is characterized by cross supply rates. Stability is reached when all supply rates are non-positive, as long as the total exchanged energy between the activated subsystem and any inactivated subsystems is finite. Passivity and L2-gain are addressed. For both cases, asymptotic stability is guaranteed under certain "negative" output feedback. Feedback invariance of passivity and a small-gain theorem are also given.